I assume you mean lnē(x) instead of "In". You should immediately see that ln(x)'s derivative, 1/x, is present too which makes the following substitution useful:
This converts the integral to:
Now I created "sqrt(1-...)" in the denominator. If we can get that "..." to be a square, then the inverse sine should ring a bell! So let's stick that 9/4 within the square and adjust the dx (instead of another substitution):
Now this is a standard integral, which yeilds arcsin of the integration variable.
I hope this is clear